Federal Reserve governor Chris Waller said Monday that the central bank needs to proceed with "more caution" when cutting rates as he absorbs recent data showing a strong job market and hotter-than-expected inflation.

"Data is signaling that the economy may not be slowing as much as desired," Waller said in a speech at Stanford University in California.

"While we do not want to overreact to this data or look through it, I view the totality of the data as saying monetary policy should proceed with more caution on the pace of rate cuts than was needed at the September meeting."

His baseline, he added, still calls for reducing rates "gradually over the next year." Waller will be watching to see whether data out before the Fed's next Nov. 6-7 policy meeting confirms or undercuts his inclination to be more cautious.

The Fed in September initiated its first rate cut in more than four years, starting with a jumbo-sized 50 basis point reduction designed to get ahead of any weaknesses in the labor market now that inflation was on its way down.

But in the weeks since that pivotal move, Fed officials have digested a warmer-than-expected inflation reading for the month of September that offered new ammunition to those at the Fed arguing for a gradual pace of cuts. A stronger-than-expected September jobs report also bolstered the position of hawks on the Fed’s interest rate-setting committee.

These voices include Fed governor Michelle Bowman, the lone dissenter on the September rate cut who wanted to move more slowly given her concerns about inflation.

Minneapolis Fed president Neel Kashkari said Monday that it’s "likely" the central bank will make "modest" interest rate reductions in the "coming quarters."

Monetary policy, he said while speaking in Argentina, remains "overall restrictive," though how restrictive is unclear to him.

The job market remains strong, he added, noting that recent data showed that a rapid weakening in that market doesn’t appear to be "imminent."

Thus, "It appears likely that further modest reductions in our policy rate will be appropriate in the coming quarters to achieve both sides of our mandate," Kashkari said.

Other Fed colleagues are now arguing for gradual cuts as well.

Atlanta Fed president Raphael Bostic told the Wall Street Journal last week that he was “totally comfortable” with holding steady at the Fed's Nov. 6-7 meeting and that he had already penciled in an estimate of just one more rate cut this year.